IB MYP 3 Mathematics 7.6 Time, Time Calculations and Time Zones Study Notes - New Syllabus

7.6 – Time, Time Calculations and Time Zones

Time is used to measure when events happen, how long they last, and the order in which events occur. We use time calculations in timetables, travel, sports, school schedules, appointments and everyday planning.

In this topic, you will learn how to convert between units of time, calculate durations, use the 24-hour clock, work with timetables, and calculate differences between time zones.

Units of Time

The main units of time used in everyday mathematics are seconds, minutes, hours, days, weeks, months and years.

 Converting Time

To convert hours into minutes, multiply by \(60\).

\(4\text{ h}=4\times60=240\text{ min}\)

To convert minutes into hours and minutes, divide by \(60\) and use the remainder as the number of minutes.

\(157\div60=2\text{ remainder }37\)

\(157\text{ min}=2\text{ h }37\text{ min}\)

Similarly:

\(367\text{ s}=6\text{ min }7\text{ s}\)

because:

\(367\div60=6\text{ remainder }7\)

Calculating with Time

When adding or subtracting time, remember that \(60\) minutes make \(1\) hour and \(60\) seconds make \(1\) minute.

For example:

\(2\text{ h }45\text{ min}+1\text{ h }35\text{ min}\)

\(=3\text{ h }80\text{ min}\)

\(=4\text{ h }20\text{ min}\)

We regroup \(60\) minutes as \(1\) hour.

When subtracting time, borrowing may be necessary.

For example:

\(5\text{ h }10\text{ min}-2\text{ h }35\text{ min}\)

\(=4\text{ h }70\text{ min}-2\text{ h }35\text{ min}\)

\(=2\text{ h }35\text{ min}\)

 Finding a Time After or Before Another Time

To find a time after an event, add the duration to the starting time. To find a time before an event, subtract the duration from the given time.

Example: A lesson begins at \(9{:}35\) am and lasts \(2\) hours \(45\) minutes.

\(9{:}35\text{ am}+2\text{ h}=11{:}35\text{ am}\)

\(11{:}35\text{ am}+45\text{ min}=12{:}20\text{ pm}\)

Therefore, the lesson finishes at \(12{:}20\) pm.

 Finding the Duration of an Event

The duration of an event is the amount of time between its starting time and finishing time.

A useful method is to break the calculation into simple intervals.

For example, find the time from \(8{:}45\) am to \(2{:}30\) pm.

\(8{:}45\text{ am}\rightarrow1{:}45\text{ pm}=5\text{ h}\)

\(1{:}45\text{ pm}\rightarrow2{:}30\text{ pm}=45\text{ min}\)

\(\therefore\text{ Duration}=5\text{ h }45\text{ min}\)

Time Calculations Across Midnight

When an event continues past midnight, the date changes.

For example, a person sleeps from \(9{:}40\) pm to \(6{:}15\) am the next morning.

\(9{:}40\text{ pm}\rightarrow12{:}00\text{ midnight}=2\text{ h }20\text{ min}\)

\(12{:}00\text{ midnight}\rightarrow6{:}15\text{ am}=6\text{ h }15\text{ min}\)

\(2\text{ h }20\text{ min}+6\text{ h }15\text{ min}=8\text{ h }35\text{ min}\)

Therefore, the person slept for \(8\) hours \(35\) minutes.

 Large Units of Time

For example:

\(6\text{ decades}=6\times10=60\text{ years}\)

\(4\text{ centuries}=4\times100=400\text{ years}\)

\(3\text{ millennia}=3\times1000=3000\text{ years}\)

 24-Hour Time

The 24-hour clock represents the hours of a day using numbers from \(00{:}00\) to \(23{:}59\). It avoids the need to use am and pm.

Converting am to 24-hour time:

\(8{:}35\text{ am}=08{:}35\)

For pm times from \(1{:}00\) pm to \(11{:}59\) pm, add \(12\) to the hour.

\(7{:}20\text{ pm}\rightarrow7+12=19\)

\(7{:}20\text{ pm}=19{:}20\)

Converting 24-hour time to 12-hour time:

For times from \(13{:}00\) to \(23{:}59\), subtract \(12\) from the hour.

\(18{:}45-12\text{ h}=6{:}45\text{ pm}\)

 Time Zones

Different places on Earth experience different times of day because the Earth rotates. Therefore, the world is divided into time zones.

Time zones are described using an offset from a reference time. A location may be ahead of or behind the reference time.

The Prime Meridian is at longitude \(0^\circ\) and passes through Greenwich. Greenwich Mean Time (GMT) has traditionally been used as a reference for time-zone calculations.

In modern notation, time zones are commonly expressed as offsets from UTC (Coordinated Universal Time).

For example, if Location A is \(+5\) hours from UTC and Location B is \(-4\) hours from UTC, then Location A is:

\(5-(-4)=9\text{ hours}\)

ahead of Location B.

 Calculating Time Between Two Time Zones

A reliable method is:

1. Write the UTC offset for each location.
2. Find the difference between the offsets.
3. Move forward if the destination is ahead.
4. Move backward if the destination is behind.
5. Check whether the date changes.

For example, suppose Location A is UTC \(+5\) and Location B is UTC \(+2\). Location A is:

\(5-2=3\text{ hours}\)

ahead of Location B.

Therefore, if it is \(10{:}00\) am in Location B:

\(10{:}00\text{ am}+3\text{ h}=1{:}00\text{ pm}\)

The local time in Location A is \(1{:}00\) pm.

 Time Zones and Travel

Travel problems involving time zones require two separate calculations:

1. Calculate the time the journey finishes in the departure location’s time.
2. Convert that finishing time to the destination’s local time.

This prevents the flight duration from being confused with the time-zone difference.

Crossing Midnight and Changing Dates

A time-zone calculation can cause the date to change.

For example, if a location is \(5\) hours ahead and the calculated time is \(22{:}30\), then:

\(22{:}30+5\text{ h}=27{:}30\)

Since a day has \(24\) hours:

\(27{:}30-24{:}00=03{:}30\)

Therefore, the correct time is \(03{:}30\) on the next day.